The present invention relates to a new and distinct strawberry cultivar designated ‘DrisStrawTwo’ and botanically known as Fragaria×ananassa. This new strawberry cultivar originated from a controlled cross between ‘Driscoll Camarillo’ (U.S. Plant Pat. No. 14,771) and ‘Driscoll Marin’ (U.S. Plant Pat. No. 15,375). The original seedling of the new cultivar was asexually propagated by stolons at a nursery in Shasta County, Calif. Propagules were transplanted to a controlled breeding plot in Ventura County, Calif. where it was identified and selected for further evaluation in October, 2002. ‘DrisStrawTwo’ was subsequently asexually propagated and underwent further testing at various locations in Monterey County, Calif. for four years. The present invention has been found to retain its distinctive characteristics through successive asexual propagations.